Internal problem ID [3988]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 11, Bernoulli
Equations
Problem number: Exercise 11.3, page 97.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
\[ \boxed {y^{\prime } x +y-y^{2} \ln \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 13
dsolve(x*diff(y(x),x)+y(x)=y(x)^2*ln(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {1}{1+c_{1} x +\ln \left (x \right )} \]
✓ Solution by Mathematica
Time used: 0.157 (sec). Leaf size: 20
DSolve[x*y'[x]+y[x]==y[x]^2*Log[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{\log (x)+c_1 x+1} \\ y(x)\to 0 \\ \end{align*}